Since the birth of his granddaughter, $19$ years ago, Thomas has deposited $$250$ at the beginning of every month into a Registered Education Savings Plan $($RESP$).$ The interest rate on the plan was $3\mathrm{.}25\%$ compounded monthly for the first $9$ years and $4\mathrm{.}00\%$ compounded monthly for the next $10$ years.

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a$.$ What was the accumulated value of the RESP at the end of $9$ years?

Round to the nearest cent

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b$.$ What was the accumulated value of the RESP at the end of $19$ years?

Round to the nearest cent

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c$.$ What was the amount of interest earned over the $19-$year period?

Round to the nearest cent

Donald invested $$1,250$ at the end of every month into an investment fund that was earning interest at $3\mathrm{.}50\%$ compounded monthly. He stopped making regular deposits at the end of $9$ years when the interest rate changed to $3\mathrm{.}75\%$ compounded quarterly. However, he let the money grow in this investment fund for the next $3$ years.

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a$.$ Calculate the accumulated balance in his investment fund at the end of $9$ years.

Round to the nearest cent

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b$.$ Calculate the accumulated balance in his investment fund at the end of $12$ years.

Round to the nearest cent

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c$.$ Calculate the amount of interest earned over the $12-$year period.

Round to the nearest cent

$3.$ Lindsey secured a lease on a machine by paying $$1,850$ as a down payment and then $$175$ at the beginning of every half$-$year for $3$ years. Assume that the cost of financing is $6\mathrm{.}96\%$ compounded semi$-$annually.

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a$.$ What was the principal amount of the loan?

Round to the nearest cent

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b$.$ What was the cost of the machine?

Round to the nearest cent

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c$.$ What was the amount of interest paid over the term?

Round to the nearest cent

$4.$ Nathan withdraws $$5,060\mathrm{.}00$ at the beginning of every month from a $$25,000\mathrm{.}00$ fund which is growing at $4\mathrm{.}08\%$ compounded monthly.

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a$.$ Calculate the number of monthly withdrawals that he can make, rounded down to include only whole $$5,060\mathrm{.}00$ withdrawals.

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b$.$ Calculate the time taken to deplete the fund. Express your answer in years and months, rounding to the nearest month.

years

months

$5.$ Kayla pays $$263\mathrm{.}25$ for a car lease at the beginning of every month for $1$ years and $5$ months at $3\mathrm{.}26\%$ compounded monthly.

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a$.$ What type of annuity is this?

Ordinary simple annuity

Ordinary general annuity

Simple annuity due

General annuity due

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b$.$ How many payments are there in this annuity?

Round up to the next payment

$6.$ Calculate the present value of a loan that could be cleared by payments of $$3,350$ at the end of every $6$ months for $7$ years if money earns $6\mathrm{.}45\%$ compounded semi$-$annually.

Round to the nearest cent

$7.$ Veronica invested $$1,800$ at the beginning of every $6$ months in an RRSP for $11$ years. For the first $9$ years it earned interest at a rate of $4\mathrm{.}20\%$ compounded semi$-$annually and for the next $2$ years it earned interest at a rate of $6\mathrm{.}40\%$ compounded semi$-$annually.

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a$.$ Calculate the accumulated value of his investment at the end of the first $9$ years.

$$52,585\mathrm{.}92$

$$52,827\mathrm{.}62$

$$38,885\mathrm{.}29$

$$39,701\mathrm{.}88$

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b$.$ Calculate the accumulated value of her investment at the end of $11$ years.

$$52,585\mathrm{.}92$

$$52,827\mathrm{.}62$

$$47,496\mathrm{.}61$

$$39,701\mathrm{.}88$

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c$.$ Calculate the amount of interest earned from the investment.

$$13,227\mathrm{.}62$

$$12,985\mathrm{.}92$

$$12,632\mathrm{.}89$

$$594\mathrm{.}73$

$8.$ Mary is leasing a vehicle worth $$16,400,$ with a down payment of $$3,000$ and equal payments at the beginning of every month for three years. What is the size of each lease payment if the cost of borrowing is $5\mathrm{.}99\%$ compounded monthly and the residual value is $$10,500?$

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Lease payment:

Round to nearest cent.